Consider the line with equation
5x – 2y = 10.
(a) Find the y-intercept for the given line.
(b)Find the slope for a line parallel to the given line.
(c) Find the slope for a line perpendicular to the given line.
Put it in slope intercept form.
y=5/2 x -5
check my thinking.
So the y will = -5 but what about the slopes of a parallel and perpendicular to the given line? I got
m= 2.5 for the parallel one, is this correct?
To find the y-intercept, we can set x = 0 and solve for y.
(a) Find the y-intercept for the given line:
Substituting x = 0 into the equation, we have:
5(0) - 2y = 10
-2y = 10
Divide both sides by -2:
y = -5
So, the y-intercept for the given line is -5.
(b) To find the slope for a line parallel to the given line, we can observe that parallel lines have the same slope. The given equation is 5x - 2y = 10, which can be rewritten as:
-2y = -5x + 10
To determine the slope, we need to express the equation in slope-intercept form (y = mx + b), where m is the slope. Divide both sides of the equation by -2:
y = (5/2)x - 5
The slope of the given line, and thus any line parallel to it, is 5/2.
(c) To find the slope for a line perpendicular to the given line, we can observe that perpendicular lines have slopes that are negative reciprocals of each other. The given equation's slope can be read from its coefficient (5/2).
The negative reciprocal of 5/2 is -2/5.
So, the slope for a line perpendicular to the given line is -2/5.
To find the y-intercept for the given line, we can set x = 0 and solve for y.
For this equation, we have:
5x – 2y = 10
Substituting x = 0, we get:
5(0) – 2y = 10
-2y = 10
y = -10/2
y = -5
Therefore, the y-intercept for the given line is -5.
To find the slope for a line parallel to the given line, we can simply use the fact that parallel lines have the same slope.
The given line is in the form 5x – 2y = 10. We can rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Start by isolating y:
-2y = -5x + 10
y = (5/2)x - 5
From this equation, we can see that the slope (m) is 5/2.
Therefore, any line parallel to the given line will also have a slope of 5/2.
To find the slope for a line perpendicular to the given line, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
The given line has a slope of 5/2. To find the negative reciprocal, we flip the fraction and change its sign:
Negative reciprocal of 5/2 = -2/5
Therefore, any line perpendicular to the given line will have a slope of -2/5.